Question

Which statement is true about the equation (x - 4)(x + 2) = 16?

The equation x- 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 - 2x - 8 = 0.
The factored form of the equation is (x + 4)(x - 6) = 0.
One solution of the equation is x = -6.
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Answer 1

C. The factored form of the equation is ( x + 4 )( x - 6 ) = 0

Answer 2

Explanation:

A) The equation x- 4 = 16 can be used to solve for a solution of the given equation.

From: x- 4 = 16, we find x= 4+16, or x=20.

Replace x=20 for the equation (x-4)(x+2)=16

we find that: (20-4)(20+2) = 16*22
`\\eq` 16

So A is wrong.

B) The standard form of the equation is x2 - 2x - 8 = 0.

(x - 4)(x + 2) = 16

or x^2 +2x -4x -8 =16

or x^2 -2x -8 -16 =0

or x^2 -2x -24=0

Then, B is wrong.

C) The factored form of the equation is (x + 4)(x - 6) = 0.

We can develop: (x + 4)(x - 6) = 0

or x^2 -6x +4x -24=0

or x^2 -2x -24 =0

So C is right.

D) One solution of the equation is x = -6.

Replace x=-6 we have (x-4)(x+2) = (-6 -4)(-6+2) = (-10)(-4) = 40
`\\eq` 16.

So D is wrong.

Finally, C is right.